Computer Science ›› 2021, Vol. 48 ›› Issue (8): 253-262.doi: 10.11896/jsjkx.200700032

• Artificial Intelligence • Previous Articles     Next Articles

Multi-agent System Based on Stackelberg and Edge Laplace Matrix

ZHANG Jie1, YUE Shao-hua2, WANG Gang2, LIU Jia-yi1, YAO Xiao-qiang2   

  1. 1 Graduate School,Air Force Engineering University,Xi'an 710054,China;
    2 School of Air-Defense and Anti-Missile,Air Force Engineering University,Xi'an 710054,China
  • Received:2020-07-06 Revised:2020-08-11 Published:2021-08-10
  • About author:ZHANG Jie,born in 1995,postgra-duate.His main research interests include combat multi-agent based on deep learning,tactical air defense & guidance command and control system.( Shao-hua,born in 1968,master,professor.Her main research interests include machine learning,command information system and intelligent command & control.
  • Supported by:
    Science Fund for Young Scholars of the National Natural Science Foundation of China(61703412),China Postdoctoral Science Foundation(2016M602996) and National Natural Science Foundation of China(61503407,61806219,61703426,61876189).

Abstract: Aiming at the problems of low efficiency,local conflict resolution and lack of practical application scenarios in the interaction model of multi-agent system in the distributed environment,this paper designs a multi-agent multi-slave interaction model based on Stackelberg game,which is applied to the interaction game between the controller and the participants in the command and control process.Firstly,through the optimization of Stackelberg game model and the multi-agent system of Stackelberg game of multiple leaders-follwers designed by multi-attribute decision-making,the closed-loop solution problem of Stackelberg game is solved by introducing a regular Riccati equation,which uses the optimization regularity of semi positive quadratic performance index.Then,based on graph theory,a multi-agent system model based on edge Laplace matrix is established to reduce the difficulty of solving complex problems.At last,numerical simulation and experimental analysis verify the efficiency and strong robustness of the model from many aspects.Moreover,it also proves that the proposed model is true and efficient.

Key words: Closed-loop solution, Distributed, Edge Laplace matrix, Multi-master and multi-slave, Stackelberg game

CLC Number: 

  • TP301.6
[1]WANG F Y.CC 5.0:Intelligent Command and Control Systems in the Parallel Age[J].Journal of Command and Control,2015,1(1):107-120.
[2]CHEN L,SHEN Y.Stochastic Stackelberg differential reinsu-rance games under time-inconsistent mean-variance framework[J].Insurance Mathematics and Economics,2019,88(4):409-444.
[3]ZHANG M Y,WANG M Y,WANG X D,et al.Research onReal-Time Task Allocation of UAV Group Collaboration Based on Improved Contract Network [J].Aero Weaponry,2019,26(4):38-46.
[4]LI X Q.Research on the Control of Hybrid H_2/H_∞ Based on Stackelberg Game Method [D].Jinan:Shandong University,2019.
[5]GALARZA-JIMENEZ F,TELLEZ-CASTRO D,SOFRONY J,et al.Cooperative Output Regulation for Multi-Agent Systems with EDMD Leader Approximation[J].IFAC Papers OnLine,2019,52(20):91-96.
[6]PIVOVARCHIKV.On multiplicity of eigenvalues in quantumgraph theory[J].Journal of Mathematical Analysis and Applications,2019,480(2):977-986.
[7]FAN Y Z,WANG Y,BAO Y H,et al.Eigenvectors of Laplacian or signless Laplacian of hypergraphs associated with zero eigenvalue[J].Linear Algebra and Its Applications,2019,579(6):244-261.
[8]OKANO T,NODA I.Adaptation Method of the ExplorationRatio Based on the Orientation of Equilibrium in Multi-Agent Reinforcement Learning Under Non-Stationary Environments[J].Journal of Advanced Computational Intelligence & Intelligent Informatics,2017,21(5):939-947.
[9]WU L L,JING Z X,WU Q H,et al.Equilibrium Interaction Strategy of Integrated Energy System Based on Stackelberg Game Model[J].Automation of Electrics Power Systems,2018,42(4):142-150,207.
[10]ZACKSENHOUSE M,NEMETS S,LEBEDEV M A,et al.Robust satisficing linear regression:Performance/robustness trade-off and consistency criterion[J].Mechanical Systems and Signal Processing,2008,23(6):1954-1964.
[11]CRETTEZ B.On Hobbes's state of nature and game theory[J].Theory and Decision,2017,83(4):499-511.
[12]WU Q,WANG F,ZHOU L G,et al.Method of Multiple Attri-bute Group Decision Making Based on 2-Dimension Interval Type-2 Fuzzy Aggregation Operators with Multi-granularity Linguistic Information[J].International Journal of Fuzzy Systems,2017,19(6):1880-1903.
[13]SOLMEYER N,DIXON R,BALU R.Characterizing the Nashequilibria of a three-player Bayesian quantum game[J].Quantum Information Processing,2017,16(6):146.
[14]GREINER D,PERIAUX J,EMPERADOR M J,et al.GameTheory Based Evolutionary Algorithms:A Review with Nash Applications in Structural Engineering Optimization Problems[J].Archives of Computational Methods in Engineering,2017,24(4):703-750.
[15]HOLMBERG E,THORE C J,KLARBRING A.Game theoryapproach to robust topology optimization with uncertain loading[J].Structural and Multidisciplinary Optimization,2017,55(4):1383-1397.
[16]LIU X K,GE Y Y,LI Y.Stackelberg games for model-free continuous-time stochastic systems based on adaptive dynamic programming[J].Applied Mathematics and Computation,2019,363:301-306.
[17]CHUGH T,SINDHYA K,HAKANEN J,et al.Handling computationally expensive multiobjective optimization problems with evolutionary algorithms:A survey[J].Soft Computing,2019,23(9):3137-3166.
[18]ZENG X L.Research on Aircraft Route Planning Method Based on Multi-Agent Co-Evolution [D].Harbin:Harbin Engineering University,2014.
[19]YAGER R R.Multi-Criteria Decision Making with Interval Criteria Satisfactions Using the Golden Rule Representative Value[J].IEEE Transactions on Fuzzy Systems,2018,26(2):1023-1031.
[20]CONWAY T J.More indefinite integrals from Riccati equations[J].Integral Transforms and Special Functions,2019,30(12):33-44.
[21]AZAD M,BABICˇ J,MISTRY M.Effects of the weighting matrix on dynamic manipulability of robots[J].Autonomous Robots,2019,43(7):1867-1879.
[22]ZHANG H,LI L,XU J,et al.Linear quadratic regulation and stabilization of discrete-time systems with delay and multiplicative noise[J].IEEE Transactions on Automatic Control,2015,60(10):2599-2613.
[23]REN Y.Research on First-Order Multi-Agent System with Va-riable Parameter Quantizer[D].Harbin:Harbin Industrial University,2013.
[24]KONG F Q,WANG D D,SHEN Q.Robust target tracking of l_1-l_2 norm combined constraint [J].Chinese Journal of Scienti-fic Instrument,2016,37(3):690-697.
[25]MARCO A,MARTíNEZ J J,VIAÑA R.Least squares prob-lems involving generalized Kronecker products and application to bivariate polynomial regression[J].Numerical Algorithms,2019,82(1):21-39.
[26]ZHANG H.Structural Characteristics of Strongly Connected K Quasi-Transitive Directed Graphs [D].Taiyuan:Shanxi University,2017.
[27]LUO W,SONG C N,XU Q X.Perturbation estimation for the parallel sum of Hermitian positive semi-definite matrices[J].Linear and Multilinear Algebra,2019,67(10):1971-1984.
[28]REN W,BEARD R W.Consensus seeking in multiagent systems under dynam-ically changing interaction topologies [J].Automatic Control,IEEE Transactionson,2005,50(5):655-661.
[29]LI C Y,QU Z H,QI D L,et al.Distributed finite-time estimation of the bounds on algebraic connectivity for directed graphs[J].Automatica,2019,107:289-295.
[30]STEGAGNO P,YUAN C Z.Distributed cooperative adaptive state estimation and system identification for multi-agent systems[J].Control Theory & Applications,IET,2019,13(6):815-822.
[31]ZHOU B,XU X T,LIU J G,et al.Information interaction model for the mobile communication networks[J].Physica A:Statistical Mechanics and its Applications,2019,525:1170-1176.
[32]MA Y M.Research on Feedback Mechanism of Online Learning Based on Metacognition[D].Chendu:Sichuan Normal University,2016.
[33]ZHANG J,WANG G,SONG Y F,et al.Optimization of Air-Defense Resource Deployment Based on Adaptive SGD-Multiagent[J].Systems Engineering and Electronic Technology,2019,41(7):1536-1543.
[34]WANG G,LI W M,HE J.Research on Resource Management of Distributed Air Defense Battlefield Based on Multi-Agent[J].Fire Control & Command Control,2003,65(2):32-34.
[35]SU J H.The Existence And Uniqueness of Solutions to Stochastic Differential Equations with Non-Lipschitz Coefficients[D].Hefei:University of Science and Technology of China,2017.
[1] LU Chen-yang, DENG Su, MA Wu-bin, WU Ya-hui, ZHOU Hao-hao. Federated Learning Based on Stratified Sampling Optimization for Heterogeneous Clients [J]. Computer Science, 2022, 49(9): 183-193.
[2] FU Li-yu, LU Ge-hao, WU Yi-ming, LUO Ya-ling. Overview of Research and Development of Blockchain Technology [J]. Computer Science, 2022, 49(6A): 447-461.
[3] YANG Ya-hong, WANG Hai-rui. DDoS Attack Detection Method in SDN Environment Based on Renyi Entropy and BiGRU Algorithm [J]. Computer Science, 2022, 49(6A): 555-561.
[4] SUN Hao, MAO Han-yu, ZHANG Yan-feng, YU Ge, XU Shi-cheng, HE Guang-yu. Development and Application of Blockchain Cross-chain Technology [J]. Computer Science, 2022, 49(5): 287-295.
[5] FENG Liao-liao, DING Yan, LIU Kun-lin, MA Ke-lin, CHANG Jun-sheng. Research Advance on BFT Consensus Algorithms [J]. Computer Science, 2022, 49(4): 329-339.
[6] TAN Shuang-jie, LIN Bao-jun, LIU Ying-chun, ZHAO Shuai. Load Scheduling Algorithm for Distributed On-board RTs System Based on Machine Learning [J]. Computer Science, 2022, 49(2): 336-341.
[7] WANG Ru-bin, LI Rui-yuan, HE Hua-jun, LIU Tong, LI Tian-rui. Distributed Distance Join Algorithm for Massive Spatial Data [J]. Computer Science, 2022, 49(1): 95-100.
[8] TANG Fei, CHEN Yun-long, FENG Zhuo. Electronic Prescription Sharing Scheme Based on Blockchain and Proxy Re-encryption [J]. Computer Science, 2021, 48(6A): 498-503.
[9] LU Yong-chao, WANG Bin-yi, HU Jiang-feng, MU Yang, REN Jun-long. Research on Integrated Electronic Time Synchronization Technology [J]. Computer Science, 2021, 48(6A): 629-632.
[10] QIAN Tian-tian, ZHANG Fan. Emotion Recognition System Based on Distributed Edge Computing [J]. Computer Science, 2021, 48(6A): 638-643.
[11] CAO Xue-fei, NIU Qian, WANG Rui-bo, WANG Yu, LI Ji-hong. Distributed Representation Learning and Improvement of Chinese Words Based on Co-occurrence [J]. Computer Science, 2021, 48(6): 222-226.
[12] ZHANG Hang, TANG Dan, CAI Hong-liang. Study on Predictive Erasure Codes in Distributed Storage System [J]. Computer Science, 2021, 48(5): 130-139.
[13] GAO Feng-yue, WANG Yan, ZHU Tie-lan. Resilient Distributed State Estimation Algorithm [J]. Computer Science, 2021, 48(5): 308-312.
[14] YUAN De-yu, CHEN Shi-cong, GAO Jian, WANG Xiao-juan. Intervention Algorithm for Distorted Information in Online Social Networks Based on Stackelberg Game [J]. Computer Science, 2021, 48(3): 313-319.
[15] ZHANG Xiao, ZHANG Si-meng, SHI Jia, DONG Cong, LI Zhan-huai. Review on Performance Optimization of Ceph Distributed Storage System [J]. Computer Science, 2021, 48(2): 1-12.
Full text



No Suggested Reading articles found!